The Rev. Jesse Jackson’s sex-scandal headache isn’t fading – the National Enquirer is hitting the stands with claims about another extramarital romance two years ago.

A month after revelations the civil-rights leader fathered a love child with a Rainbow/PUSH Coalition executive, the tabloid reports he was intimate with another aide.

But this time, instead of a confirmation and apology from Jackson, the story has prompted a strongly worded denial from the woman in question.

The Enquirer, quoting a former coalition worker, claims Jackson had a “sexual relationship” with a Rainbow Coalition funding-office staffer.

The tabloid claims the married minister showered the 31-year-old woman, now divorced, with cash gifts and arranged for her to get a $12,000 raise during a wage freeze.

The woman, who works in the Chicago-based organization’s funding office, said the story isn’t true.

“I categorically deny the scurrilous and frivolous allegations,” she said in a statement. “I am offended and will address the violations of my privacy in a different forum with my lawyers.

“But the violation and harassment of my family has got to stop. Offering my ex-husband $25,000, which thank God he refused, is trashy and unethical.”

The Enquirer was the first to report on Jackson’s romance with ex-professor Karin Stanford and their baby daughter. The story opened the floodgates of negative news.

In its latest report, the tabloid said the married minister first “hit on” the funding-office aide in a closed-door meeting.

“I know, because she came right back and told me about it,” Jennifer Williams, described as a friend who worked in the coalition’s membership office until the fall of 1999, told the tabloid.

“She was really upset. She said Reverend touched her. She said, ‘He started feeling on me.’ She said he’d given her money and she opened her hand.

“It was $500 in hundred-dollar bills. I said, ‘Go give it back . . . You don’t want to put yourself in that position.'”

The Enquirer said the woman didn’t return the money and continued seeing Jackson, meeting him at the Chicago Hilton and accompanying him on out-of-town trips.

“Every time you looked up, he was dishing out money to her; $700 here, $500 there, $300,” Williams said, adding that Jackson gave the woman $300 for a dress on her birthday.

The Enquirer quoted another ex-employee as confirming the gifts.

The tab said the woman also got a raise from $36,000 to $48,000 last year and it quoted Benita Crittle, a woman identified as a friend of the coalition’s former chief financial officer, Jim Chavis, as saying:

“Jim told me that he suspected that something was going on between Jackson [and the woman]. He said she wasn’t so terribly talented to deserve a big raise, and that it came while Rainbow had a wage freeze.”

The current CFO of the coalition, Billy Owens, disputed that account, saying he made an “independent decision” to give the worker a raise when he was hired.